Find the surface area of the prism.&nbsp;

Total Surface Area of a Triangular Prism FormulaAtot=Atop+Abot+Alat Lateral Surface Area of a Triangular Prism FormulaAlat=h(a+b+c)=6(4+5+3)=6×12=72 m2Bottom Surface Area of a Triangular Prism FormulaAbot=14(a+b+c)(b+c−a)(c+a−b)(a+b−c)=14(4+5+3)(5+3−4)(3+4−5)(3+5−4)=6 m2Top Surface Area of a Triangular Prism FormulaAtop=14(a+b+c)(b+c−a)(c+a−b)(a+b−c)=14(4+5+3)(5+3−4)(3+4−5)(4+5−3)=6 m2So, total surface area Atot=72+6+6 =83 m2

Key to "Find the surface area of the prism."

High School
Geometry
High school geometry
Solid Geometry

Answered question

2022-02-08

Find the surface area of the prism.

Answer & Explanation

nick1337

Expert2022-03-08Added 777 answers

Total Surface Area of a Triangular Prism Formula

$A_{t o t} = A_{t o p} + A_{b o t} + A_{l a t}$

Lateral Surface Area of a Triangular Prism Formula

$A_{l a t} = h (a + b + c) = 6 (4 + 5 + 3) = 6 \times 12 = 72 m^{2}$

Bottom Surface Area of a Triangular Prism Formula

$A_{b o t} = \frac{1}{4} \sqrt{(a + b + c) (b + c - a) (c + a - b) (a + b - c)}$

$= \frac{1}{4} \sqrt{(4 + 5 + 3) (5 + 3 - 4) (3 + 4 - 5) (3 + 5 - 4)}$

$= 6 m^{2}$

Top Surface Area of a Triangular Prism Formula

$A_{t o p} = \frac{1}{4} \sqrt{(a + b + c) (b + c - a) (c + a - b) (a + b - c)}$

$= \frac{1}{4} \sqrt{(4 + 5 + 3) (5 + 3 - 4) (3 + 4 - 5) (4 + 5 - 3)}$

$= 6 m^{2}$

So, total surface area

$A_{t o t} =$ $72 + 6 + 6$

$= 83 m^{2}$

Do you have a similar question?

Recalculate according to your conditions!

New Questions in High school geometry

The distance between the centers of two circles C1 and C2 is equal to 10 cm. The circles have equal radii of 10 cm.
A part of circumference of a circle is called
A. Radius
B. Segment
C. Arc
D. Sector
The perimeter of a basketball court is 108 meters and the length is 6 meters longer than twice the width. What are the length and width?
What are the coordinates of the center and the length of the radius of the circle represented by the equation $x^{2} + y^{2} - 4 x + 8 y + 11 = 0$ ?
Which of the following pairs of angles are supplementary?
128,62
113,47
154,36
108,72
What is the surface area to volume ratio of a sphere?
An angle which measures 89 degrees is a/an _____.
right angle
acute angle
obtuse angle
straight angle
Herman drew a 4 sided figure which had only one pair of parallel sides. What could this figure be?
Trapezium
Parallelogram
Square
Rectangle
Which quadrilateral has: All sides equal, and opposite angles equal?
Trapezium
Rhombus
Kite
Rectangle
Karen says every equilateral triangle is acute. Is this true?
Find the number of lines of symmetry of a circle.
A. 0
B. 4
C. 2
D. Infinite
The endpoints of a diameter of a circle are located at (5,9) and (11, 17). What is the equation of the circle?
What is the number of lines of symmetry in a scalene triangle?
A. 0
B. 1
C. 2
D. 3
How many diagonals does a rectangle has?
A quadrilateral whose diagonals are unequal, perpendicular and bisect each other is called a.
A. rhombus
B. trapezium
C. parallelogram

Didn't find what you were looking for?